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Principles and arguments for the teaching of rational numbers in different contexts
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0003-2896-0890
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Teachers do not solely determine how a mathematics content matter is taught. Rather, this determination takes place within different contexts, which teachers need to negotiate. To understand how a teacher’s teaching of rational numbers was enabled and constrained by surrounding contexts I studied four contexts, where a teacher group, textbooks and the national curriculum constituted parts of an ecology of a teacher’s teaching practice. I drew on Chevallard and ATD to analyse the technology of didactic praxeologies. In this analysis, inferred arguments for how rational numbers should be taught in terms of how sub-constructs of rational numbers were distributed within the different contexts. To analyse the theory of didactic praxeologies, traces of principles were inferred, using Bishop’s mathematical values as a framework. These analyses showed a very homogenous ecology, where the four contexts privileged the similar aspects of rational numbers and the same mathematical values. Seeing how aspects of rational numbers were expressed in relation to teaching activities, it was possible to discuss how the privileged mathematical values may have affected how rational numbers were presented and dealt with. If the principles and arguments that generate teaching activities are privileged the same way in several contexts, we need to include a broader context than teachers’ classrooms in professional development strategies. Teachers need to engage in other sources than textbooks and official curricula and to have the opportunities to discuss the political dimension of their teaching practice as well as how other contexts influence the teaching of specific content matter.

Keywords [en]
Teachers, Teaching, ATD, Praxeology
National Category
Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:su:diva-160663OAI: oai:DiVA.org:su-160663DiVA, id: diva2:1252389
Available from: 2018-10-01 Created: 2018-10-01 Last updated: 2018-10-22Bibliographically approved
In thesis
1. The Ecology of Mary’s Mathematics Teaching: Tracing Co-determination within School Mathematics Practices
Open this publication in new window or tab >>The Ecology of Mary’s Mathematics Teaching: Tracing Co-determination within School Mathematics Practices
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Teachers’ mathematics teaching has been studied in many different ways. Such studies not often include more contexts than the teacher’s teaching practice. An assumption in this thesis is that in order to create a deeper understanding of mathematics teachers’ teaching we also need to study the contexts around mathematics teachers, and in relation to each other. Together such contexts create an environment for teachers’ teaching. The determination of how mathematics is taught is not decided in any of the contexts alone. Rather, all contexts participate in the determination of how mathematics is taught and teachers need to negotiate how different contexts privilege both mathematics and mathematics education. In this study, I have studied one teacher’s, Mary’s, teaching practice as well as three contexts from her close environment, the teacher group she participated in, the textbooks she used, and the national curriculum she was bound to follow. To study how mathematics and mathematics teaching was privileged in the four studied contexts became a way to trace how the contexts participate in the determination, in short, their co-determination of how mathematics is taught.

With an aim to deepen the understanding of how the environment of a teacher’s teaching enables and constrains mathematics teaching, the four contexts were studied in relation to each other in different ways, in four studies. First, the context of Mary’s mathematics teaching was studied in relation to the teacher group in how the justifications of Mary’s mathematics teaching was constituted in relation to a teacher group discussion. Second, Mary’s teaching of problem-solving was studied in relation to how problem-solving was privileged in both mathematics textbook and national curriculum. Third, praxeology was explored as an analytical tool to understand how mathematics was privileged in teaching practice in relation to the privileging of mathematics in textbooks. Fourth, all four contexts were studied to trace arguments and principles for teaching rational numbers and how these enable and constrain the teaching of rational numbers.

To address these different contexts, ATD as described by Chevallard was adopted. In ATD, the environment of contexts with influence of teachers’ practices, is described as an ecology with levels that co-determine each other. The studied contexts represented some of these levels of co-determination. The privileging of mathematics and mathematics teaching was studied from a varied data material. Data from Mary’s teaching practice was transcripts of classroom observations and interviews. Data from the teacher group was transcripts of teacher meetings. Data from the textbook context was the textbooks and teacher guides Mary used. Data from the context of the national curriculum was the mathematics syllabus accompanied with clarifying and explanatory comments.

The analyses revealed a strong resemblance of the mathematical communication between the different contexts. They all emphasised similar approaches to problem-solving, aspects of rational numbers, mathematical values, or explanations of angles. Mary, however, anchored her arguments for mathematics teaching in partially different theoretical principles than those privileged in the ecology. Theoretical principles were not explicitly communicated in any context. They were inferred from the communication. An implication generated by these findings is the importance for teachers to engage in the principles behind the privileging expressed in contexts they need to negotiate. These principles need to be discussed and challenged. Another implication is the relevance of allowing for teachers to engage in research literature, and to have influences from other sources than their immediate contexts. The thesis also point to the need to study textbooks and national curriculum, not in terms of how they are enacted by teachers, but what they privilege. By doing so teachers practices may be understood in the sense of what teachers have to negotiate, where the consequence is a deeper understanding of constraints and affordances for teachers’ teaching practices.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics and Science Education, Stockholm University, 2018. p. 115
Series
Doctoral thesis from the department of mathematics and science education ; 19
Keywords
Mathematics teaching, Mathematics teachers, ATD, Co-determination, Praxeology
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-160693 (URN)978-91-7797-450-5 (ISBN)978-91-7797-451-2 (ISBN)
Public defence
2018-11-23, Vivi Täckholmsalen (Q-salen), NPQ-huset, Svante Arrhenius väg 20, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.

Available from: 2018-10-29 Created: 2018-10-02 Last updated: 2018-10-29Bibliographically approved

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